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Czechoslovak Mathematical Journal

, Volume 60, Issue 1, pp 161–172 | Cite as

Global structure of positive solutions for superlinear 2mth-boundary value problems

  • Ruyun Ma
  • Yulian An
Article
  • 47 Downloads

Abstract

We consider boundary value problems for nonlinear 2mth-order eigenvalue problem
$$ \begin{gathered} ( - 1)^m u^{(2m)} (t) = \lambda a(t)f(u(t)),0 < t < 1, \hfill \\ u^{(2i)} (0) = u^{(2i)} (1) = 0,i = 0,1,2,...,m - 1. \hfill \\ \end{gathered} $$
. where aC([0, 1], [0, ∞)) and a(t 0) > 0 for some t 0 ∈ [0, 1], fC([0, ∞), [0, ∞)) and f(s) > 0 for s > 0, and f 0 = ∞, where \( \mathop {\lim }\limits_{s \to 0^ + } f(s)/s \). We investigate the global structure of positive solutions by using Rabinowitz’s global bifurcation theorem.

Keywords

multiplicity results Lidstone boundary value problem eigenvalues bifurcation methods positive solutions 

MSC 2010

34B10 34G20 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2010

Authors and Affiliations

  • Ruyun Ma
    • 1
  • Yulian An
    • 2
  1. 1.Department of MathematicsNorthwest Normal UniversityLanzhouP.R. China
  2. 2.Department of MathematicsLanzhou Jiaotong UniversityLanzhouP.R. China

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